Might be the word "heavy" refers to something specific about the hardware or capabilities of the ship type, and is not related to mass at all. Much like in WWII, where "heavy" meant main guns between 6.1 and 8 inches in caliber, and "light" meant smaller guns, and things such as ship displacement, length, or the number of guns had no effect on the designation. Perhaps the armament that defines a "light" cruiser in 2260s terms has recently become antiquated but the terminology has not?
Again, I'd like to point out that FJ's list is unlikely to be complete in any sense. There are all those ships that don't fall into the Class I category (else why have the category?). Then there are all those things that were authorized (and presumably built, launched and commissioned) before the Constitution class and no doubt still remain in operation. Taking these into consideration, we must conclude that Kirk's "twelve like her" must carry a very specific meaning, and Starfleet at the time of that statement operated more than twelve heavy cruisers.
Except perhaps in the FJverse where Starfleet had sprung up fairly recently and had been making do with "original" ships right until TOS. But FJverse isn't in synch with the canon Trek universe any more, if it ever was.
Timo Saloniemi